Alternating Current MCQ Quiz - Objective Question with Answer for Alternating Current - Download Free PDF

Explanation:

Alternating Current

Definition: Alternating Current (AC) is a type of electrical current in which the magnitude of the current changes continuously and its direction reverses periodically. This behavior contrasts with Direct Current (DC), where the current flows steadily in one direction.

Working Principle:

In AC, the flow of electrons alternates between moving forward and backward within the conductor. This alternating behavior is caused by the periodic reversal of the voltage polarity across the circuit. The frequency of the AC determines how often the current reverses direction per second. For example, in most countries, the standard frequency of AC is 50 Hz or 60 Hz, meaning the current reverses direction 50 or 60 times per second.

Characteristics:

• Magnitude: The magnitude of AC varies continuously with time, typically following a sinusoidal waveform. The voltage and current rise and fall in a smooth, cyclic manner.
• Direction: The direction of AC changes periodically, reversing back and forth, unlike DC, which flows in a single direction.

Advantages:

• Efficient Power Transmission: AC can be easily transformed to higher or lower voltages using transformers, making it ideal for transmitting electricity over long distances with minimal losses.
• Wide Application: AC is the standard form of electricity used in homes, offices, and industries because most electrical devices and appliances are designed to work with AC.
• Flexible Generation: AC can be generated using devices like alternators, which are simpler and more efficient than DC generators for large-scale electricity production.

Disadvantages:

• Complexity in Circuits: AC circuits require additional components like capacitors and inductors to manage voltage and current, which makes them slightly more complex than DC circuits.
• Safety Concerns: Due to its alternating nature, AC can be more dangerous than DC at high voltages, as the periodic reversal can cause more severe effects on the human body.

Applications:

• Domestic and industrial power supply.
• Operation of electrical appliances such as fans, refrigerators, and televisions.
• Powering large-scale machinery and equipment in factories.

Correct Option Analysis:

The correct option is:

Option 1: Changes continuously; changes periodically

This option accurately describes the behavior of an alternating current. The magnitude of AC changes continuously, typically in a sinusoidal pattern, and the direction of current flow reverses periodically, following the frequency of the AC system.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: Does not change; remains the same

This description corresponds to Direct Current (DC), not Alternating Current (AC). In DC circuits, the current flows steadily in one direction, and its magnitude remains constant over time. Therefore, this option is incorrect for describing AC.

Option 3: Does not change; changes periodically

This option is inconsistent. If the magnitude of the current does not change, it cannot be categorized as AC since the defining characteristic of AC is the continuous variation in magnitude and periodic reversal in direction. This statement is contradictory and does not apply to AC.

Option 4: Changes continuously; remains the same

This option partially describes the behavior of AC but fails to account for the periodic reversal of direction. While the magnitude of AC does change continuously, its direction also reverses periodically. Hence, this option is incomplete and incorrect.

Conclusion:

Understanding the fundamental characteristics of Alternating Current (AC) is essential for differentiating it from Direct Current (DC). The correct option, as explained, accurately captures the behavior of AC, where the magnitude changes continuously and the direction reverses periodically. This unique property makes AC suitable for widespread use in power transmission, domestic applications, and industrial operations, despite its associated complexities and safety considerations.

Concept:

The Phasor diagram of a purely inductive circuit is:

​

• In a purely inductive circuit, the current lags voltage by 90°
• The power factor in a purely inductive circuit is given by cosϕ, where ϕ is the angle between current and voltage.
• Therefore, cosϕ = cos 90° = 0

Explanation:

The power in a purely inductive circuit is given by:

P = VI cosϕ

where P = Active power

V = Voltage

I = Current

cosϕ = Power factor

∵ cosϕ = 0

∴ P = VI × (0)

P = 0

Therefore the power is zero in a purely inductive circuit.

Additional Information The reactive power in a purely inductive circuit is given by:

Q = VI sinϕ

∵ cosϕ = 0

∴ sinϕ = 1

Q = V× I × (1)

Q = V× I = Maximum

• A pure inductive circuit is an energy-absorbing circuit, hence it only absorbs lagging reactive power.
• It does not dissipate any active power.

Concept:

Reactive power (Q) = V I sinϕ

Where,

V = Voltage in volt

I = Current in ampere

ϕ = phase difference between voltage & current

Calculation:

Voltage (V) = 230 V

Current (I) = 5 A

Phase difference (ϕ) = 30°

Q = 230 × 5 × sin30°

Concept:

In a star-connected circuit,

  & 

In a delta-connected circuit,

  & 

Where,

VL = Line voltage

VP = Phase voltage

IL = Line current

IP = Line current

Calculation:

For 200 V phase voltage in a star connected circuit, then its line voltage is

Concept

The complex power is given by:

S = VI^*

Also, P = S cosϕ 

and Q = S sinϕ 

where, S = Apparent power 

V = Voltage

I* = Conjugate of current

P = Active power

Q = Reactive power

Calculation

Given, V_s = 100 V

R = 3Ω 

X_L = 4Ω 

The current is given by:

P = 2000 cos(53.13°)

P = 2000 × 0.6

P = 1200 W

The correct answer is option 1): 1.11

The form factor is defined as the ratio of the RMS value to the average value of an alternating quantity.

F.F. (Form factor) = 

Crest Factor ‘or’ Peak Factor is defined as the ratio of the maximum value to the R.M.S value of an alternating quantity.

C.F. ‘or’ P.F. =

 For a sinusoidal waveform:

Form Factor = 1.11

Crest Factor = 1.414

Concept:

Reactive power (Q) = V I sinϕ

Where,

V = Voltage in volt

I = Current in ampere

ϕ = phase difference between voltage & current

Calculation:

Voltage (V) = 230 V

Current (I) = 5 A

Phase difference (ϕ) = 30°

Q = 230 × 5 × sin30°

Concept:

In AC circuits, the power factor is defined as the ratio of the real power flowing to the load to the apparent power in the circuit.

Power factor = cos ϕ

Where ϕ is the angle between voltage and current.

If the current lags the voltage, the power factor will be lagging.

If the current leads the voltage, the power factor will be leading.

Power factor = cos ϕ = R/Z

Where,

R = resistance

Z = impedance

X = reactance

The power factor is unity when the circuit is purely resistive.

Calculation:

Power factor = R/Z = 10/10 = 1 (unity)

The correct option is 1

Concept:

Voltage v = 100 sin (90 πt - \(\frac {π} {6}\))

Current i = 100 sin (90 πt - \(\frac {\pi} {6}\))

The phase difference between voltage and current is 0 only in the resistive part. there is no inductive or capacitive part.

w = angular frequency =  = 

 f =  = 45 HZ, resistive

Additional point

At a resonance 

In a series resonance circuit current vs frequency graph for the series resonance circuit

• Line voltage (line-to-line voltage) in a poly-phase system is the voltage between any two given phases.
• While the phase voltage is the voltage between any given phase and neutral.
• In delta connected circuits,
1. Line voltage is equal to phase voltage
2. Line current is equal to √3 times the phase current with a lag of 30°.
• In star connected circuits,
1. Line voltage is equal to √3 times the phase voltage with a lead of 30°.
2. Line current is equal to phase current.
• Note that neutral is available in star connection but not in delta connection.

• Inductive reactance (X_L), capacitive reactance (X_C), impedance (Z) & resistance (R) are calculated/rated in ohm (Ω).
• Reactive power (Q) is calculated/rated in VAR.
• Current (i) is calculated/rated in ampere.
• Active power (P) is calculated in watt.

In pure inductive circuit, current lags the voltage by 90°.

In pure capacitive circuit, current leads the voltage by 90°.

In R - L circuits, current lags the voltage but it is not exactly 90°.

In R - C circuits, current leads the voltage but it is not exactly 90°.

Concept:

For a sinusoidal alternating waveform

• Peak to peak value of voltage (V_p-p) = 2 (Peak value)
• The peak value of voltage (V_p) = √2 V_rms
• RMS value of voltage
• The average value of voltage

Calculation:

V_rms = 250 V

V_p = √2 × 250 V

V_p-p = 2 × √2 × 250

∴ V_p-p = 707 V

For a balanced system the phase difference between all three phases is 120°.

For delta connection,

Line voltage is equal to phase voltage, i.e. V_L = V_ph

Line current is equal to the phasor difference of the current in two phases connected to the line, i.e.

Current in line R = I_R – I_B

Current in line Y = I_Y – I_R

Current in line B = I_B – I_Y

Where, I_R, I_Y, and I_B are the phase current in delta connection.

For a balanced system, the phasor diagram is given below.

Where,

V_R, V_Y, and V_B are the phase voltages

I_R, I_Y, and I_B are the phase currents

I_R, I_Y, and I_B are the line currents

• Line voltage lags behind phase current by an angle equal to the power factor angle φ.
• The angle between the line voltage and line current is (30° - φ)
• The angle between line current and phase current is 30°

The correct answer is option 1):Root Mean square Value

Concept:

• RMS value of voltage is said to be s the square root of the mean square of instantaneous values of the voltage signal
• AC voltages (and currents) are always given as RMS values because this allows a sensible comparison to be made with steady DC voltages
• RMS is Root Mean square Value 
• The RMS voltage (RMS) of a sinusoidal waveform is obtained by multiplying the peak voltage value by 0.7071

Vrms =

where

Vm is the maximum voltage